Generating Z-number based on OWA weights using maximum entropy

Kang, Bingyi; Deng, Yong; Hewage, Kasun; Sadiq, Rehan

doi:10.1002/int.21995

Cited by 79 publications

(45 citation statements)

References 36 publications

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“…Many math tools are presented to model uncertainty, such as Z numbers, [53][54][55] D numbers, [56][57][58][59][60][61] and entropy model. [62][63][64][65][66][67] Among then, evidence theory is widely used due to its efficiency to deal with uncertainty.…”

Section: Preliminariesmentioning

confidence: 99%

Dependent evidence combination based on decision‐making trial and evaluation laboratory method

Deng

2019

Int J Intell Syst

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Dempster‐Shafer is widely used to address the problems of uncertainty. One assumption mentioned in this theory is that the distribution of information should be independent. In practice, the requirement cannot be fulfilled. One of the efficient methods to deal with dependent evidence is to calculate the correlation discounting. However, existing coefficient can only be applied to show the direct relation between evidence A and B but do not take the indirect relationship into consideration. To address this issue, in this paper, a new method to combine dependent evidence based on decision‐making trial and evaluation laboratory is presented, not only considering the relation between evidence A and B and the relation between evidence B and C, but also considering the transitive influence between evidence A and C. Finally, the experiments on some benchmark data sets are illustrated to show the efficiency of the proposed method.

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Section: Preliminariesmentioning

confidence: 99%

Dependent evidence combination based on decision‐making trial and evaluation laboratory method

Deng

2019

Int J Intell Syst

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“…Fuzzy logic was developed by Zadeh and Mamdani and Assilian, based on which the concept of approximate reasoning was introduced and showed that vague logical statements enable the formation of algorithms that can use vague data to derive vague inferences. Many theories have been promoted by this method, such as Dempster‐Shafer theory, Z‐numbers, and fuzzy reasoning . The definition of fuzzy sets is given as follows:…”

Section: Fuzzy Sets and Ivfssmentioning

confidence: 99%

“…Fuzzy logic was developed by Zadeh 26 and Mamdani and Assilian, 27 based on which the concept of approximate reasoning was introduced and showed that vague logical statements enable the formation of algorithms that can use vague data to derive vague inferences. Many theories have been promoted by this method, such as Dempster-Shafer theory, [28][29][30][31] Z-numbers, [32][33][34] and fuzzy reasoning. [35][36][37] The definition of fuzzy sets is given as follows: Note that the membership function can take any value from the closed interval [0, 1], and the greater μ x ( ) A is, the greater the truth of the statement that element x belongs to set A is.…”

Section: Fuzzy Sets and Ivfssmentioning

confidence: 99%

On interval‐valued fuzzy decision‐making using soft likelihood functions

Fei

2019

Int J Intell Syst

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Multicriteria decision‐making approaches have been studied very widely in recent years and are frequently used in many real‐life applications. To select the optimal alternative that satisfies the multicriteria, effective aggregation methods are crucial in the decision‐making process. The soft likelihood functions (SLF) developed by Yager is introduced as preliminaries of our research, which is a flexible aggregation approach of probabilistic evidence in the context of forensic crime investigations. Motivated by SLF, in this study, a novel aggregation method is proposed based on ordered weighted averaging operator under interval‐valued fuzzy environments. To improve the performance of the new aggregation method, the reliability is taken into account in the decision‐making process from two perspectives. The first is the reliability of assessment value, including certainty and compatibility, for discounting assessment information; the second is human reliability for redefining SLF. Some numerical examples are given to demonstrate the proposed decision approach. And the reliability‐based aggregation method is illustrated more reasonable than the one without considering reliability.

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“…Clearly, using expressions (23) and (25), we can obtain directly the optimal weights given a specified degree of orness Ω by first computing the Lagrange multiplier λ 2 from Equation (25) and then by computing the Lagrange multiplier λ 1 from (22), thus solving the constrained optimization problem in (8)-(9).…”

Section: Filev and Yager's Analytic Construction Of Meowa Weightsmentioning

confidence: 99%

“…Applications of the maximum entropy approach can be found in various fields, see, for instance, Chang et al, Liaw et al, Yusoff and Merigó‐Lindahl, Chuu, He et al, and Kang et al. Two very recent applications of the maximum entropy method are described in Kim and Ahn and Brunelli and Fedrizzi.…”

Section: Introductionmentioning

confidence: 99%

Maximum entropy ordered weighted averaging in the binomial decomposition framework

2018

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We consider the maximum entropy constrained optimization problem associated with ordered weighted averaging (OWA) in the binomial decomposition framework. We begin by reviewing the analytic solution of the maximum entropy method proposed by Filev and Yager in 1995, and later by Fullér and Majlender in 2001. Next, we briefly review the binomial decomposition framework, which allows for an alternative parametric description of the OWA functions. The values of the binomial coefficients α j , j = 1 ,-0.15em … , n are uniquely determined by the weighting structure of the OWA function. We observe that for low orness values normalΩ ∈ [ 0 , 0.5 ], the optimal weights are decreasing, whereas they are increasing for high orness values normalΩ ∈ [ 0.5 , 1 ]. Moreover, we notice that the optimal values of the first and last weights have a wide range in [ 0 , 1 ], whereas the values of the other weights have more restricted ranges. As for the optimal α j , j = 1 , … , n coefficients, we find that their behavior with respect to orness values normalΩ ∈ [ 0 , 1 ] is very different for low/high orness. We illustrate graphically the optimal α j , j = 1 , … , n coefficients in two parts, first for low orness values normalΩ ∈ [ 0 , 0.5 ] and then for high orness values normalΩ ∈ [ 0.5 , 1 ]. We observe that the optimal α j , j = 1 , … , n for low orness values normalΩ ∈ [ 0 , 0.5 ] are all nonnegative and take values in the unit interval, independently of the dimension n. On the contrary, the optimal values of the α j , j = 1 , … , n coefficients for high orness values normalΩ ∈ [ 0.5 , 1 ] depend strongly on the dimension n, both in the complexity of their distribution and in the amplitude of their scale.

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Generating Z-number based on OWA weights using maximum entropy

Cited by 79 publications

References 36 publications

Dependent evidence combination based on decision‐making trial and evaluation laboratory method

Dependent evidence combination based on decision‐making trial and evaluation laboratory method

On interval‐valued fuzzy decision‐making using soft likelihood functions

Maximum entropy ordered weighted averaging in the binomial decomposition framework

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